Download - anuitas
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ANUITAS
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PENGERTIAN
2
Anuitas adalah cara pembayaran pinjaman dengan sejumlah uang yang sama setiap masa bunga.
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Pinjaman sebesar M dibayar dengan n kali anuitas dgn suku bunga i. Besarnya anuitas yang dibayarkan digambarkan dalam bagan berikut.
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A(1+i)-1 AA(1+i)-2 AA(1+i)-3 AA(1+i)-4 AA(1+i)-5 A
.
.
. ….A(1+i)-n A M = A{(1+i)-1 + (1+i)-2 + (1+i)-
3+ (1+i)-4+ (1+i)-5 +… (1+i)-n} M = A an]i --> A = M/ an]i
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RUMUS-RUMUS
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RUMUS ANUITAS
ni)(iMA
11
1. A = an + bn
2. A = a1 (1 + i)n
3.atau A = Anuitas
an = angsuran periode ke-na1 = Angsuran periode ke-1
bn = bunga periode ke- n(1 + i)n = faktor bunga majemuk
atau faktor bunga anuitas
naM 1.A
na1
A ni)(i
11 ni)(i
11
ni)(i
11 na1
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RUMUS ANGSURANna1
A ni)(i
11 ni)(i
11
1. an = ak (1 + i) n – k
2. an = A - bn
A = Anuitas an = angsuran periode ke-n bn = bunga periode ke-n ak = angsuran periode ke-k
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RUMUS BUNGAna1
A ni)(i
11 ni)(i
11
1. bn = i. Mn 2. bn = A – an A = Anuitas an = angsuran periode ke-n bn = bunga periode ke-n i = suku bunga Mn = modal awal periode ke-n
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RUMUS SISA ANGSURAN
na1
A ni)(i
11 ni)(i
11
1.
2. Sn = Mn - an
Sn = Sisa angsuran periode ke-n bm+1 = bunga periode ke-(m+1) i = suku bunga Mn = modal awal periode ke-n an = angsuran periode ke-n
ibS 1m
n
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Contoh 1:Tentukanlah besar anuitas dari table pelunasan berikut:
ThnKe-
Pinjaman awal
Anuitas = A Sisa pinjaman
Bunga 2% Angsuran
1 1.000.000 - 6.355 -2 - 1.872,99 - 87.162,9
0
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Jawab :
A = an + bn
A = a1 + b1 = 6.355 + (2% x 1.000.000)
= 6.355 + 20.000= Rp 26.355,00
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Contoh soal 2:Ibu meminjam uang yang akan dibayar secara anuitas bulanan dengan suku bunga majemuk 5% sebulan selama 10 bulan. Jika besar angsuran pertama yang dibayarkan Rp 1.590.091,50. tentukanlaha. besar angsuran ke-5 b. besar anuitas c. besar bunga ke-5d. sisa angsuran ke-4
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Jawab :Dik. i = 5%a1 = RP 627.453,95 n = 10
a. besar angsuran ke-5 an = ak ( 1+ i)n-k
a5 = a1 ( 1+ i)5-1
a5 = 1590091,50 ( 1+ 0.05)4
= 1590091,50 x 1,21550625
= 1932766,16
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b. besar anuitas A = a1 (1+i)n
A = 1590091,50 (1,05)10
= 2590091,50
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c. besar bunga ke-5
bn = A – an
b5 = A – a5
= 2590091,50– 1932766,16 = 657,325.34
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ib
S 1mn
ib
S 54
0.05657.325,34S4
d. sisa angsuran ke-4
= 14,987,236.55
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MEMBUAT TABEL ANUITAS
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Contoh soal :
Buatlah tabel rencana angsuran anuitas dari Modal Rp 20.000.000 dengan suku bunga 5% dan masa pelunasan 10 bulan
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Jawab :
A = atau
= 2.590.091.50
1005,1105,0000.000.20
x
61391325,011000000
38608675.01000000
ni)(iMA
11na
M 1.A
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BlKe
Pinjaman A = 2,590,091.50 Sisa
Pinjaman Bunga 5% Angsuran
1 20,000,000.00 1,000,000.00 1590091.50
18409908.50
2 18,409,908.50 920,495.43 1669596.07
416740312.4
3
3 16,740,312.43 837,015.62 1753075.87
814987236.5
5
4 14,987,236.55 749,361.83 1840729.67
213146506.8
8
5 13,146,506.88 657,325.34 1932766.15
511213740.7
2
6 11,213,740.72 560,687.04 2029404.46
3 9184336.26
7 9,184,336.26 459,216.81 2130874.68
6 7053461.57
8 7,053,461.57 352,673.08 2237418.42
1 4816043.15
9 4,816,043.15 240,802.16 2349289.34
2 2466753.81
10 2,466,753.81 123,337.69 2466753.80
9 0.00
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Contoh soal :
Diketahui Modal Rp 10.000.000 dengan suku bunga 6% dan masa pelunasan 4 bulan.Tentukanlah :
a. Besar anuitasb. tabel rencana angsuran
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Jawab :
A = atau
= 2.895.914,92
406,1106,0000.000.10
x
79209366,011000000
20790634,01000000
ni)(iMA
11na
M 1.A
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Tabel Angsuran Anuitas